The main aim of this article is to offer a predictive method to determine the most significant values of a sky component on the floor of circular or square courtyards of variable sizes under overcast sky conditions to be calculated quickly and precisely. Firstly, analytical geometry is used to calculate the sky component on the floor of the courtyards under study considering the variable height/width ratios. Empirical expressions are offered subsequently to fit the results obtained using analytical geometry, thus establishing the predictive method. (C) 2013 Elsevier Ltd. All rights reserved.